Tara bought 4 souvenirs during 2 days of vacation. After 8 days of vacation, how many total souvenirs will Tara have bought? Solve using unit rates

Rule of trigonometric functions:-

sin a = cos(90 - a)

Here a = 90°.

sin 90 = cos (90 - 90)

1 = cos 0.

cos 0 = 1.

So the cos 0 = 1.

Answer:

Step-by-step explanation:

If sin 90 = 1

then cos 0 will be

as we know that

cosx = sin(90-x)

If we plug x = 0 ,

cos0  = sin 90 = 1

2x+2y=6

5x+2y =4

Multiply eq 1 by 5 and equation 2 by -2

10x+10y = 30

-10x - 4y = -8

Now adding we get

6y = 22

Divide by 2

3Y =11

Answer:

3/47 is rational because it is a ratio of two integers.

Answer:

f(1) = -2

Step-by-step explanation:

Each point is (x, f(x)).

The point (1, f(1)) is given as (1, -2), so f(1) = -2.

Answer:

f(1) = -2

Step-by-step explanation:

Wrong answer = x

Correct answer = y

Total questions: x+y = 30

Rewrite for x: x = 30-y

Total points:

-8x + 7y = 0

replace x with 30-y

-8(30-y) + 7y = 0

Simplify:

-240 + 8y + 7y = 0

Combine like terms:

-240 + 15y = 0

Add 240 to each side:

15y = 240

Divide both sides by 15:

y = 240 / 15

y = 16

There were 16 correct answers

30-16 = 14 wrong answers.

ANSWER

The correct answer is A.

EXPLANATION

The volume of a cube is given by

[tex]V=l^3[/tex]

First we find the volume of the cube with side length [tex]\frac{3}{4}cm[/tex]

[tex]V_{Cube}=(\frac{3}{4})^3[/tex]

[tex]V_{Cube}=\frac{27}{64} cm^3[/tex]

Next, we find the volume of the cubic block with side length [tex]\frac{3}{8}cm[/tex]

[tex]V_{Block}=(\frac{3}{8})^3[/tex]

[tex]V_{Block}=\frac{27}{512} cm^3[/tex]

We divide the volume of the cube by the volume of the block to get the number of cubic blocks

[tex]Number\: of \: blocks=\frac{\frac{27}{64}} {\frac{27}{512}}[/tex]

[tex]Number\: of \: blocks=\frac{27}{64} \times \frac{512}{27}[/tex]

[tex]Number\: of \: blocks=\frac{1}{1} \times \frac{8}{1}=8[/tex]

Answer:

The correct answer is option A.

8 blocks are needed to fill the box.

Step-by-step explanation:

Given data:

Side length of a block = 3/8 cm

Side length of main block = 3/4 cm

How many blocks are needed to fit in main blocks = ?

Solution:

Volume  = length³

Volume of one simple block = (3/8)³ = 27/512 cm³

Volume of one Main block = (3/4)³ = 27/64 cm³

Blocks are needed to fit in main blocks = (27/64) ÷ (27/512) = 8

                                                            Answer = 8 blocks

Hence 8 simple small blocks of one side length 3/8 cm will needed to fit in the main block of side length 3/4 cm.

Answer:

From the comments below we see the missing part of the question is "in how many days will the ant farm consume 3 apples?"

The answer is 18.

Step-by-step explanation:

We will use a proportion to solve this.  It takes 3 days to consume 1/2 of an apple; this gives us the ratio

3/0.5

We want to know how many days, x, it will take to consume 3 apples; this gives us the ratio

x/3

Together this gives us the proportion

3/0.5 = x/3

Cross multiply:

3(3) = 0.5(x)

9 = 0.5x

Divide both sides by 0.5:

9/0.5 = 0.5x/0.5

18 = x

The ant farm will take 18 days to consume 3 apples.

Given that,

According to above information, calculation of data are as follows,

[tex]X = (3 \div 0.5) \times 3\\\\X = 6 \times 3[/tex]

X = 18

So, Total number of days required is 18 days.

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R= c-s/t. For c

Switch the equation to have c on left side

C-s/t= r

Now multiply t both sides

C-s= r(t)

C-s= rt

Now add s both sides to get your answer

C= s+rt

the answer is 16.7 because you need to  do 60/360

The answer is 16.67%

Explanation:

Number of customers who visited in the first week = 360

Number of customers who visited in the second week = 300

Number of customers decreased in the second week =

[tex]360-300=60[/tex]

So, the percentage change of the number of customers that visited the store in the first week to the number of customers that visited the store in the second week will be = [tex]\frac{60}{360}*100 =16.67[/tex]

Coterminal angles are angles in standard position (angles with the initial side on the positive x -axis) that have a common terminal side.

Coterminal angles are angles that have the same terminal sides in standard position.

Anytime we complete a full cycle( a complete revolution) we come back to the same terminal side.

Therefore to find all angles which are coterminal with [tex]-271\degree[/tex] we keep adding or subtracting [tex]360\degree[/tex].

For the given interval, that is, [tex]0\degree[/tex] to [tex]360\degree[/tex],

We add [tex]360\degree[/tex] so that we can obtain an angle coterminal with [tex]-271\degree[/tex] within this interval.

This means that

[tex]-271\degree[/tex] is coterminal with [tex]360\degree + \: -271\degree=89\degree[/tex]

Hence the correct and answer is D

ANSWER

[tex]x=\frac{14.5\degree}{3}+120\degree n\:or\:x=\frac{165.5\degree}{3} +120\degree n[/tex], for [tex]n\ge 0[/tex], where [tex]n[/tex] is an integer.

EXPLANATION

We want to solve the trigonometric equation;

[tex]Sin(3x)=\frac{1}{4}[/tex]

Since sine ratio is positive, it means the argument,[tex](3x)[/tex] is either the first quadrant or second quadrant.

This implies that;

[tex](3x)=arcsin(\frac{1}{4})[/tex]

[tex](3x)=14.5\degree[/tex] in the first quadrant.

Or

[tex](3x)=180\degree-14.5\degree=165.5\degree[/tex] in the second quadrant.

Since the sine function has a period of [tex]360\degree[/tex], The general solution is given by

[tex](3x)=14.5\degree+360\degree n\:or\:(3x)=165.5\degree +360\degree n[/tex],for [tex]n\ge 0[/tex], where [tex]n[/tex] is an integer.

Dividing through by 3, we obtain the final solution to be;

[tex]x=\frac{14.5\degree}{3}+120\degree n\:or\:x=\frac{165.5\degree}{3} +120\degree n[/tex], for [tex]n\ge 0[/tex], where [tex]n[/tex] is an integer.

Answer:

Step-by-step explanation:

we have to find the dot product here.

From the formula of dot product of vectors,

we know-

if  X=<a,b,c>   and    Y=<d,e,f>

Then dot product of  X and Y is-

X.Y=ad+be+cf

Here, we get

v=<2 , -8 , -8>

and   w=<-2 , 6 , -5>

So, the dot product is-

v . w=2(-2)+(-8)(6)+(-8)(-5)

    =-4-48+40

    =-52+40

   =-12

So,  

v . w= -12

Answer:

-12

Step-by-step explanation:

we have to find the dot product here.

From the formula of dot product of vectors,

we know-

if  X=<a,b,c>   and    Y=<d,e,f>

Then dot product of  X and Y is-

X.Y=ad+be+cf

Here, we get

v=<2 , -8 , -8>

and   w=<-2 , 6 , -5>

So, the dot product is-

v . w=2(-2)+(-8)(6)+(-8)(-5)

   =-4-48+40

   =-52+40

  =-12

So,  

v . w= -12

Answer:

D. Yermin

Step-by-step explanation:

\sqrt(0.50) = 0.70710678

When rounded go to 0.7

Answer:It’s D

That’s the answer because I did this test before and got it right

We know that if m and n are parallel, then we know that they have the same slope. We can call it x in this case.

Since we know that p is a perpendicular transversal, then we know it is the opposite and reciprocal of m. Therefore, we can label it as -1/x.

Since p = -1/x and n = x, we can tell they are perpendicular.

Parallel lines m and n, with transversal p, imply that if p is perpendicular to m (forming a 90-degree angle), it must also be perpendicular to n because parallel lines have the same inclination. Thus, the angle between n and p also has to be 90 degrees.

In the scenario presented, we're dealing with parallel lines m and n, and a transversal, p. The fact that p is perpendicular to m implies that the angle between m and p is 90 degrees. Now, since m and n are parallel, this means they have the same angle of inclination. So, the angle between n and p is also 90 degrees. This essentially means p is perpendicular to n as well.

Parallel lines have the property that they never intersect and are always equidistant. In geometry, when a line crosses two or more other lines, it is called a transversal. And when a line is perpendicular to another, it forms a 90-degree or right angle with the other line.

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Answer:  There are 138 short sleeves t-shirts.

Step-by-step explanation:

Given : In August Emily's clothing store sold 460 shirts with the ratio of short sleeve to long sleeve being 3:7.

Let the number of short sleeves shirts be 3x and the number of long sleeves shirts be 7x.

Then, according to the given question,  we have

[tex]7x+3x=460\\\\\Rightarrow\ 10x=460\\\\\Rightarrow\ x=46[/tex]

Now, the number of short sleeves shirt = 3(46)=138

Hence , there are 138 short sleeves shirts.

15 i think sorry if its wrong

The husband earns $42,000 per year.

Let's denote the husband's earnings as H.

According to the problem, the wife earns 16,000 less than twice what her husband earns. So, the wife's earnings can be represented as (2H - 16,000).

We know that together they earn 110,000 per year. This can be written as:

H + (2H - 16,000) = 110,000

Combining like terms, this equation simplifies to:

3H - 16,000 = 110,000

Add 16,000 to both sides to solve for H:

3H = 126,000

Divide both sides by 3:

H = 42,000

Therefore, the husband earns $42,000 per year.

Answer: x = 3, -5

Step-by-step explanation:

2 |x + 1| + 3 = 11

              -3   -3

2 |x + 1|       = 8

÷2               ÷2

  | x + 1 |    = 4

x + 1 = 4       or        x + 1 = -4

    -1   -1                       -1   -1

x       = 3       or        x      = -5

33 hope this helps thanks

Answer:

44

Step-by-step explanation:

The answer is 44 because 66-22=44, 44+22=66 44 is twice of 22

Distributive property

-8*4=-32          -8*9x=-72x

-32-72x=7(-2-11x)

7(-2)=-14      7(-11x)=-77x

-32-72x=-14-77x

Combine Like Terms

-32+14=-18       -77x+72x=-5x

-18=-5x

Divide both sides by -5 and theres your answer

Answer,

56

Hope this helps :-)

Hello there!

This question is super easy to me.

You had to find the prime factorization of 14.

7*2=14

Next, you had to find the prime factorization of 8.

2*2*2=8

7*2*2*2=56

Answer⇒⇒⇒56

The least common multiple of 14 and 8 is 56.

Hope this helps!

Thank you for posting your question at here on Brainly.

-Charlie

You moved the decimal place, but didn't account for that in your exponent. It  should no longer be 10.

The answer is 1.035*10¹¹

This kind of problems are solved using Bernoulli's distribution. Everytime you have a win/lose scenario, and you know the probability [tex] p[/tex] of winning, and you want [tex]k[/tex] successes over [tex]n[/tex] trials, you have the following probability:

[tex]\displaystyle P(k\text{ successes over }n\text{ trials}) = \binom{n}{k}p^k(1-p)^{n-k} [/tex]

You want the probability of having at least three successes, i.e. you are interested in the cases k=3 and k=4. The corresponding probabilities are

[tex]\displaystyle P(3 \text{ successes}) = \binom{4}{3}0.6^3 \cdot 0.4 = 4\cdot 0.216 \cdot 0.4 = 0.3456[/tex]

[tex]\displaystyle P(4 \text{ successes}) = \binom{4}{4}0.6^4 = 0.1296 [/tex]

So, the total probability is [tex] 0.3456+0.1296 = 0.4752[/tex]

12 inches is equivalent to 1 foot. So 12 times 4 = 48. So, the answer is b because then u know that its a little more than 48.

Hope this helped! Comment if u have questions. :)

Well to find how much 12 biscuits cost, you must first find how much each biscuit costs. Therefore, you divide 80p by 2, and get 40p. Then multiply 40p by 12 (the total amount of biscuit). You get the answer, which is 480p.

The value of s from the given equation is -1.5.

The given equation is 0.5s+1=7+4.5s.

We solve the given equation for s.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity.

Now, the given equation can be solved as follows:

0.5s+1=7+4.5s

⇒0.5s-4.5s=7-1

⇒-4s=6

⇒s=-6/4

⇒s=-1.5

Therefore, the value of s is -1.5.

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By using LCM, the result is-

Number between 10 and 20 divisible by 2, 3 and 9 = 18

What is LCM of two numbers?

LCM means Lowest Common multiple. LCM of two numbers a and b is the lowest numbers which is divisible by both a and b

LCM can be calculated by division method and prime factorization method.

Also there is an important formula relating HCF and LCM

HCF [tex]\times[/tex] LCM = Product of two numbers

Here,

The number which is divisible by 2, 3 and 9 = LCM of 2, 3 and 9.

2 = 2

3 = 3

9 = 3 [tex]\times[/tex] 3

LCM = [tex]2 \times 3 \times 3[/tex] = 18

Next number divisible by 2, 3 and 9 = 18  + 18 = 36

But 36 does not lie between 10 and 20

So number between 10 and 20 divisible by 2, 3 and 9 = 18

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